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Speak for yourself! (Posted on 2004-05-14) Difficulty: 3 of 5
When you are trying to get to Truth Town, you get to No Knaves Town, a city comprised of only Liars and Knights. Each of the three forks leading away from the town (not including the one you came from) leads to a different city.

There are 6 people around. Wanting to know who is what so you can ask them which fork to take, you ask them who is a liar and who is a knight.

A: C would say that B is a liar
B: D would say that C is a knight
C: E would say that F is a liar
D: C would say that A is a knight

Tired of these responses, you ask what fork leads to Truth Town.

E: The left fork leads to Truth Town
F: The middle fork leads to Truth Town

Which fork should you take to get to Truth Town?

See The Solution Submitted by Gamer    
Rating: 4.0000 (11 votes)

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Solution Another way | Comment 4 of 16 |
If X says "Y would say Z is a liar", either one or three of X, Y and Z must be a liar. On the other hand, if X says "Y would say Z is a knight", then either zero or two of them must be liars.

Thus, among C, E and F there are one or three liars. Let's suppose C is a knight. Among A, C and B there are one or three liars; since C isn't one, either A or B (but not both) is a liar. Among B, D and C, there are zero or two liars, and among D, C and A there rae also zero or two liars. If A is a liar, then D must also be one, and then B also has to be a liar, which it cannot be. If B is a liar, we also conclude that A has to be one, what he isn't.

C must be a liar. Thus, E and F are both liars or both knights. Since the latter cannot be (since E and F disagree) they are both liars, and you should take the right road.
  Posted by Federico Kereki on 2004-05-14 19:05:31

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